Reversible‽
I bought one of these before my last trip and just ordered another in a different colorway. Made of two layers of very light fabric, they feel light but drape nicely. Tucked, untucked. Brest pocket on both sides. It sounds silly, but it's great! (Note that the photos don't display the second pattern well at all. Look closely at the rolled-up sleeves to see what's on the other side.
https://www.target.com/p/men-s-reversible-long-sleeve-button-down-shirt-goodfellow-co/-/A-87259317